Numerical analysis of liquid fraction in solid–liquid phase transformation of semisolid alloy

Abstract

The non-linear mathematical expression of liquid fraction in solid–liquid phase transformation of semisolid alloy was derived by thermodynamic equations, and the numerical solution of the non-linear mathematical expression was obtained by the Gauss Newton iteration algorithm. The solid–liquid phase transformation of hypereutectic Al–20Si–3Fe–1Mn–4Cu–1Mg alloy was studied by differential scanning calorimetry, and it was used for the expression reliability validation and compared with the Scheil linear regression expression. The results showed that the liquid fraction of the semisolid alloy was not increased linearly with the heating temperature increasing, but increased non-linearly, which was not consistent with the Scheil expression, and the growth rate of liquid fraction was not entirely the same in different temperature ranges. The non-linear mathematical expression data fit well with the experimental data, and the non-linear mathematical expression had a smaller discrete degree and higher credibility compared with the Scheil linear regression expression. The relationship of liquid fraction and heating temperature of the semisolid alloy can be reflected by means of the non-linear mathematical expression in the case of solid–liquid phase transformation.

Keywords:

• Semisolid processing
• Liquid fraction
• Non-linear mathematical expression
• Thermodynamics
• Numerical analysis

Acknowledgements

This work was supported by the Science and Technology Research Program of Shenyang, China (grant no. 20092625-2) and the Science and Technology Research Program of Inner Mongolia University for the Nationalities, China (grant no. NMD1221).